Question

Two wells (A and B) are drilled in rocks that have the same porosity, but the rocks around well A have a higher permeability than those around well B. Suppose both wells are pumped at the same rate. Which statement is true? a) Well A will have a larger cone of depression. b) Well B will have a larger cone of depression. c) The cone of depression will be the same for both wells.

Short answer

b) Well B will have a larger cone of depression.

Step-by-step solution

Understanding Porosity and Permeability

Porosity is a measure of how much space within a rock is void or open, and permeability indicates how easily fluids can flow through a rock. In this problem, both well A and B are drilled in rocks with the same porosity but with different permeabilities.

Examining Cone of Depression

The 'cone of depression' refers to the decrease in water table elevation around a pumping well. The size of the cone of depression is affected by the permeability of the surrounding rock, with higher permeability leading to a smaller cone for the same pumping rate.

Analyzing Pumping Rate and Rock Properties

Since both wells are pumped at the same rate and well A is in rock with higher permeability, the water can flow more easily to well A without causing a large drop in the water table. Conversely, well B, with lower permeability, will experience a larger drawdown area, or cone of depression, because the water doesn't flow as easily.

Conclusion Based on Analysis

Given that well A allows water to flow more easily due to higher permeability, well B will naturally have a larger cone of depression, as it cannot supply water as efficiently from the surrounding areas when pumped at the same rate.

Key concepts

Porosity

Porosity refers to the measure of void spaces present within a rock or sediment, essentially indicating how much of the rock's volume is made up of these spaces. It's a key concept in hydrogeology because it helps predict how much water a rock can hold. The more porous a rock, the greater the amount of water it can store. For example, if a rock has a porosity of 20%, it means 20% of its volume consists of empty spaces where water can reside.
Porosity is influenced by several factors:

• Grain Size: Smaller grains typically pack more tightly than larger ones, impacting the porosity.
• Compaction: More compact rocks tend to have less porosity as the grains are tightly pressed together.
• Sorting: Well-sorted rocks, consisting of similar sized grains, typically have higher porosity compared to poorly sorted rocks.

Knowing porosity helps in assessing groundwater storage capabilities but doesn't provide information on how easily water can move through these spaces.

Permeability

Permeability, unlike porosity, measures a rock's ability to transmit water. Even if two rocks have the same porosity, they may vastly differ in how easily fluids can pass through them. This is primarily because permeability is dependent on the connectivity of those void spaces.
Key factors affecting permeability include:

• Crack Connections: Rocks with interconnected cracks or channels tend to have higher permeability.
• Pore Size: Larger pores usually increase permeability as they allow easier flow of water.
• Fluid Viscosity: Less viscous liquids flow more easily, impacting permeability measurements.

High permeability means water can flow freely through the rock, leading to efficient water supply and reduced cone of depression when pumped. On the contrary, a low permeability rock will restrict water flow, making the water drainage around the well less effective.

Cone of Depression

The cone of depression is a term used to describe the funnel-shaped lowering of the water table around a pumping well. As a well pumps water, it creates a drawdown area due to the decrease in water table elevation. The shape and extent of this 'cone' depend significantly on the permeability of the surrounding rock.
In rocks with high permeability, like those around well A, water replenishes the well quickly, leading to a smaller and less pronounced cone of depression. Conversely, in low-permeability rocks, such as those around well B, water moves slowly. Thus, a well must draw from a larger area to maintain the same pumping rate. This results in a larger cone of depression.
Understanding the cone of depression is crucial because it can affect nearby water wells and ecological systems. Properly managing a well’s extraction rate and accounting for surrounding geological conditions are vital to ensuring the sustainability of groundwater resources.